Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Predictability Enables Parallelization of Nonlinear State Space Models
Authors: Xavier Gonzalez, Leo Kozachkov, David Zoltowski, Kenneth Clarkson, Scott Linderman
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We validate our claims through extensive experiments, providing practical guidance on when nonlinear dynamical systems can be efficiently parallelized. |
| Researcher Affiliation | Collaboration | Xavier Gonzalez Stanford University EMAIL Leo Kozachkov IBM Research EMAIL David M. Zoltowski Stanford University EMAIL Kenneth L. Clarkson IBM Research EMAIL Scott W. Linderman Stanford University EMAIL |
| Pseudocode | Yes | Algorithm 1 Numerically Stable Computation of Largest Lyapunov Exponent (LLE) |
| Open Source Code | Yes | Our code is at https://github.com/lindermanlab/predictability_enables_parallelization |
| Open Datasets | Yes | On nine chaotic flows from the dysts benchmark dataset [35], Table 1 shows that while DEER converges prohibitively slowly on chaotic systems, it converges rapidly on stable observers of these systems, in accordance with our theory that predictability implies parallelizability. |
| Dataset Splits | No | The paper does not explicitly provide training/test/validation dataset splits. It describes generating data (mean-field RNN, Langevin dynamics) or using pre-defined systems (dysts) for evaluation, not for model training with traditional splits. For example, it mentions rolling out trajectories for "20 different random seeds" or for a "sequence length T = 1000". |
| Hardware Specification | Yes | In Appendix K.3, we provide additional experiments in this setting. We parallelize the sequential rollout with other optimizers like quasi-Newton and gradient descent, and observe that the number of steps these optimizers take to converge also scales with the LLE. We also record wallclock times on an H100, and observe that DEER is faster than sequential by an order of magnitude in predictable settings, but slower by an order of magnitude in unpredictable settings. |
| Software Dependencies | No | The paper mentions using FP64 for experiments but does not specify versions of programming languages, libraries, or other software components. |
| Experiment Setup | Yes | We rolled out trajectories from a mean-field RNN with step size 1 for 20 different random seeds. The dynamics equations follow the form st+1 = Wtanh(st) + ut, for mild sinusoidal inputs ut. We have st RD, where in our experiments D = 100. In particular, we draw each entry Wij iid N(0, g2/D), where g is a scalar parameter. We then set Wii = 0 for all i (no self-coupling of the neurons). We use 50 values of T from 9 to 9999 (log spaced) to make Figure 2 (Center). We highlight T = 1000 in Figure 2 (Right). For each value of g, we ran gradient descent with the following set of step sizes α: 0.01, 0.1, 0.25, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0. For each value of g, we then pick the step size α that results in the fastest convergence of gradient descent. For the smallest value of g = 0.5, we use α = 0.6; for g = 0.6, we use α = 0.5; and for all other values of g, we use α = 0.25. We use a larger tolerance of L(s)/T 10 4 to declare convergence. |